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/****************************************************************************** |
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* Top contributors (to current version): |
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* Gereon Kremer |
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* |
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* This file is part of the cvc5 project. |
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* |
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* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS |
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* in the top-level source directory and their institutional affiliations. |
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* All rights reserved. See the file COPYING in the top-level source |
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* directory for licensing information. |
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* **************************************************************************** |
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* |
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* Unit tests for the CAD module for nonlinear arithmetic. |
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*/ |
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#ifdef CVC5_USE_POLY |
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#include <poly/polyxx.h> |
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#include <iostream> |
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#include <memory> |
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#include <vector> |
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#include "test_smt.h" |
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#include "theory/arith/nl/cad/cdcac.h" |
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#include "theory/arith/nl/cad/lazard_evaluation.h" |
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#include "theory/arith/nl/cad/projections.h" |
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#include "theory/arith/nl/cad_solver.h" |
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#include "theory/arith/nl/nl_lemma_utils.h" |
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#include "theory/arith/nl/poly_conversion.h" |
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#include "theory/arith/theory_arith.h" |
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#include "theory/rewriter.h" |
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#include "theory/theory.h" |
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#include "theory/theory_engine.h" |
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#include "util/poly_util.h" |
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namespace cvc5::test { |
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using namespace cvc5; |
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using namespace cvc5::theory; |
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using namespace cvc5::theory::arith; |
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using namespace cvc5::theory::arith::nl; |
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NodeManager* nodeManager; |
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class TestTheoryWhiteArithCAD : public TestSmt |
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{ |
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protected: |
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void SetUp() override |
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{ |
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TestSmt::SetUp(); |
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d_realType.reset(new TypeNode(d_nodeManager->realType())); |
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d_intType.reset(new TypeNode(d_nodeManager->integerType())); |
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Trace.on("cad-check"); |
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nodeManager = d_nodeManager; |
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} |
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Node dummy(int i) const { return d_nodeManager->mkConst(Rational(i)); } |
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Theory::Effort d_level = Theory::EFFORT_FULL; |
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std::unique_ptr<TypeNode> d_realType; |
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std::unique_ptr<TypeNode> d_intType; |
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const Rational d_zero = 0; |
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const Rational d_one = 1; |
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}; |
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poly::AlgebraicNumber get_ran(std::initializer_list<long> init, |
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int lower, |
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int upper) |
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{ |
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return poly::AlgebraicNumber(poly::UPolynomial(init), |
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poly::DyadicInterval(lower, upper)); |
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} |
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Node operator==(const Node& a, const Node& b) |
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{ |
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return nodeManager->mkNode(Kind::EQUAL, a, b); |
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} |
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Node operator>=(const Node& a, const Node& b) |
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{ |
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return nodeManager->mkNode(Kind::GEQ, a, b); |
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} |
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Node operator+(const Node& a, const Node& b) |
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{ |
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return nodeManager->mkNode(Kind::PLUS, a, b); |
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} |
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Node operator*(const Node& a, const Node& b) |
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{ |
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return nodeManager->mkNode(Kind::NONLINEAR_MULT, a, b); |
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} |
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Node operator!(const Node& a) { return nodeManager->mkNode(Kind::NOT, a); } |
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Node make_real_variable(const std::string& s) |
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{ |
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SkolemManager* sm = nodeManager->getSkolemManager(); |
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return sm->mkDummySkolem( |
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s, nodeManager->realType(), "", SkolemManager::SKOLEM_EXACT_NAME); |
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} |
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Node make_int_variable(const std::string& s) |
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{ |
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SkolemManager* sm = nodeManager->getSkolemManager(); |
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return sm->mkDummySkolem( |
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s, nodeManager->integerType(), "", SkolemManager::SKOLEM_EXACT_NAME); |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_univariate_isolation) |
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{ |
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poly::UPolynomial poly({-2, 2, 3, -3, -1, 1}); |
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auto roots = poly::isolate_real_roots(poly); |
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EXPECT_TRUE(roots.size() == 4); |
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EXPECT_TRUE(roots[0] == get_ran({-2, 0, 1}, -2, -1)); |
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EXPECT_TRUE(roots[1] == poly::Integer(-1)); |
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EXPECT_TRUE(roots[2] == poly::Integer(1)); |
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EXPECT_TRUE(roots[3] == get_ran({-2, 0, 1}, 1, 2)); |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_multivariate_isolation) |
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{ |
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poly::Variable x("x"); |
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poly::Variable y("y"); |
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poly::Variable z("z"); |
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poly::Assignment a; |
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a.set(x, get_ran({-2, 0, 1}, 1, 2)); |
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a.set(y, get_ran({-2, 0, 0, 0, 1}, 1, 2)); |
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poly::Polynomial poly = (y * y + x) - z; |
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auto roots = poly::isolate_real_roots(poly, a); |
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EXPECT_TRUE(roots.size() == 1); |
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EXPECT_TRUE(roots[0] == get_ran({-8, 0, 1}, 2, 3)); |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_univariate_factorization) |
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{ |
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poly::UPolynomial poly({-24, 44, -18, -1, 1, -3, 1}); |
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auto factors = square_free_factors(poly); |
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std::sort(factors.begin(), factors.end()); |
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EXPECT_EQ(factors[0], poly::UPolynomial({-1, 1})); |
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EXPECT_EQ(factors[1], poly::UPolynomial({-24, -4, -2, -1, 1})); |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_projection) |
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{ |
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// Gereon's thesis, Ex 5.1 |
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poly::Variable x("x"); |
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poly::Variable y("y"); |
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poly::Polynomial p = (y + 1) * (y + 1) - x * x * x + 3 * x - 2; |
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poly::Polynomial q = (x + 1) * y - 3; |
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auto res = cad::projectionMcCallum({p, q}); |
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std::sort(res.begin(), res.end()); |
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EXPECT_EQ(res[0], x - 1); |
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EXPECT_EQ(res[1], x + 1); |
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EXPECT_EQ(res[2], x + 2); |
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EXPECT_EQ(res[3], x * x * x - 3 * x + 1); |
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EXPECT_EQ(res[4], |
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x * x * x * x * x + 2 * x * x * x * x - 2 * x * x * x - 5 * x * x |
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- 7 * x - 14); |
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} |
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poly::Polynomial up_to_poly(const poly::UPolynomial& p, poly::Variable var) |
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{ |
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poly::Polynomial res; |
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poly::Polynomial mult = 1; |
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for (const auto& coeff : coefficients(p)) |
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{ |
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if (!is_zero(coeff)) |
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{ |
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res += mult * coeff; |
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} |
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mult *= var; |
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} |
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return res; |
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} |
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TEST_F(TestTheoryWhiteArithCAD, lazard_simp) |
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{ |
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Node a = d_nodeManager->mkVar(*d_realType); |
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Node c = d_nodeManager->mkVar(*d_realType); |
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Node orig = d_nodeManager->mkAnd(std::vector<Node>{ |
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d_nodeManager->mkNode(Kind::EQUAL, a, d_nodeManager->mkConst(d_zero)), |
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d_nodeManager->mkNode( |
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Kind::EQUAL, |
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d_nodeManager->mkNode( |
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Kind::PLUS, |
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d_nodeManager->mkNode(Kind::NONLINEAR_MULT, a, c), |
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d_nodeManager->mkConst(d_one)), |
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d_nodeManager->mkConst(d_zero))}); |
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{ |
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Node rewritten = Rewriter::rewrite(orig); |
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EXPECT_NE(rewritten, d_nodeManager->mkConst(false)); |
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} |
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{ |
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Node rewritten = Rewriter::callExtendedRewrite(orig); |
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EXPECT_EQ(rewritten, d_nodeManager->mkConst(false)); |
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} |
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} |
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#ifdef CVC5_USE_COCOA |
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TEST_F(TestTheoryWhiteArithCAD, lazard_eval) |
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{ |
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poly::Variable x("x"); |
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poly::Variable y("y"); |
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poly::Variable z("z"); |
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poly::Variable f("f"); |
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poly::AlgebraicNumber ax = get_ran({-2, 0, 1}, 1, 2); |
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poly::AlgebraicNumber ay = get_ran({-2, 0, 0, 0, 1}, 1, 2); |
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poly::AlgebraicNumber az = get_ran({-3, 0, 1}, 1, 2); |
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cad::LazardEvaluation lazard; |
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lazard.add(x, ax); |
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lazard.add(y, ay); |
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lazard.add(z, az); |
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poly::Polynomial q = (x * x - 2) * (y * y * y * y - 2) * z * f; |
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lazard.addFreeVariable(f); |
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auto qred = lazard.reducePolynomial(q); |
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EXPECT_EQ(qred, std::vector<poly::Polynomial>{f}); |
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} |
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#endif |
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TEST_F(TestTheoryWhiteArithCAD, test_cdcac_1) |
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{ |
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Options opts; |
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Env env(NodeManager::currentNM(), &opts); |
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cad::CDCAC cac(env, {}); |
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poly::Variable x = cac.getConstraints().varMapper()(make_real_variable("x")); |
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poly::Variable y = cac.getConstraints().varMapper()(make_real_variable("y")); |
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cac.getConstraints().addConstraint( |
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4 * y - x * x + 4, poly::SignCondition::LT, dummy(1)); |
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cac.getConstraints().addConstraint( |
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4 * y - 4 + (x - 1) * (x - 1), poly::SignCondition::GT, dummy(2)); |
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cac.getConstraints().addConstraint( |
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4 * y - x - 2, poly::SignCondition::GT, dummy(3)); |
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cac.computeVariableOrdering(); |
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auto cover = cac.getUnsatCover(); |
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EXPECT_TRUE(cover.empty()); |
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std::cout << "SAT: " << cac.getModel() << std::endl; |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_cdcac_2) |
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{ |
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Options opts; |
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Env env(NodeManager::currentNM(), &opts); |
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cad::CDCAC cac(env, {}); |
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poly::Variable x = cac.getConstraints().varMapper()(make_real_variable("x")); |
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poly::Variable y = cac.getConstraints().varMapper()(make_real_variable("y")); |
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cac.getConstraints().addConstraint(y - pow(-x - 3, 11) + pow(-x - 3, 10) + 1, |
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poly::SignCondition::GT, |
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dummy(1)); |
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cac.getConstraints().addConstraint( |
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2 * y - x + 2, poly::SignCondition::LT, dummy(2)); |
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cac.getConstraints().addConstraint( |
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2 * y - 1 + x * x, poly::SignCondition::GT, dummy(3)); |
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cac.getConstraints().addConstraint( |
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3 * y + x + 2, poly::SignCondition::LT, dummy(4)); |
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cac.getConstraints().addConstraint( |
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y * y * y - pow(x - 2, 11) + pow(x - 2, 10) + 1, |
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poly::SignCondition::GT, |
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dummy(5)); |
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cac.computeVariableOrdering(); |
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auto cover = cac.getUnsatCover(); |
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EXPECT_TRUE(!cover.empty()); |
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auto nodes = cad::collectConstraints(cover); |
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std::vector<Node> ref{dummy(1), dummy(2), dummy(3), dummy(4), dummy(5)}; |
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EXPECT_EQ(nodes, ref); |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_cdcac_3) |
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{ |
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Options opts; |
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Env env(NodeManager::currentNM(), &opts); |
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cad::CDCAC cac(env, {}); |
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poly::Variable x = cac.getConstraints().varMapper()(make_real_variable("x")); |
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poly::Variable y = cac.getConstraints().varMapper()(make_real_variable("y")); |
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poly::Variable z = cac.getConstraints().varMapper()(make_real_variable("z")); |
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cac.getConstraints().addConstraint( |
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x * x + y * y + z * z - 1, poly::SignCondition::LT, dummy(1)); |
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cac.getConstraints().addConstraint( |
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4 * x * x + (2 * y - 3) * (2 * y - 3) + 4 * z * z - 4, |
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poly::SignCondition::LT, |
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dummy(2)); |
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cac.computeVariableOrdering(); |
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auto cover = cac.getUnsatCover(); |
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EXPECT_TRUE(cover.empty()); |
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std::cout << "SAT: " << cac.getModel() << std::endl; |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_cdcac_4) |
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{ |
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Options opts; |
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Env env(NodeManager::currentNM(), &opts); |
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cad::CDCAC cac(env, {}); |
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poly::Variable x = cac.getConstraints().varMapper()(make_real_variable("x")); |
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poly::Variable y = cac.getConstraints().varMapper()(make_real_variable("y")); |
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poly::Variable z = cac.getConstraints().varMapper()(make_real_variable("z")); |
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cac.getConstraints().addConstraint( |
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-z * z + y * y + x * x - 25, poly::SignCondition::GT, dummy(1)); |
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cac.getConstraints().addConstraint( |
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(y - x - 6) * z * z - 9 * y * y + x * x - 1, |
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poly::SignCondition::GT, |
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dummy(2)); |
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cac.getConstraints().addConstraint( |
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y * y - 100, poly::SignCondition::LT, dummy(3)); |
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cac.computeVariableOrdering(); |
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auto cover = cac.getUnsatCover(); |
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EXPECT_TRUE(cover.empty()); |
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std::cout << "SAT: " << cac.getModel() << std::endl; |
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} |
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void test_delta(const std::vector<Node>& a) |
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{ |
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Options opts; |
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Env env(NodeManager::currentNM(), &opts); |
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cad::CDCAC cac(env, {}); |
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cac.reset(); |
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for (const Node& n : a) |
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{ |
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cac.getConstraints().addConstraint(n); |
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} |
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cac.computeVariableOrdering(); |
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// Do full theory check here |
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auto covering = cac.getUnsatCover(); |
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if (covering.empty()) |
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{ |
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std::cout << "SAT: " << cac.getModel() << std::endl; |
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} |
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else |
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{ |
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auto mis = cad::collectConstraints(covering); |
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std::cout << "Collected MIS: " << mis << std::endl; |
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Assert(!mis.empty()) << "Infeasible subset can not be empty"; |
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Node lem = NodeManager::currentNM()->mkAnd(mis).negate(); |
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std::cout << "UNSAT with MIS: " << lem << std::endl; |
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} |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_delta_one) |
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{ |
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std::vector<Node> a; |
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Node zero = d_nodeManager->mkConst(Rational(0)); |
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Node one = d_nodeManager->mkConst(Rational(1)); |
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Node mone = d_nodeManager->mkConst(Rational(-1)); |
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Node fifth = d_nodeManager->mkConst(Rational(1, 2)); |
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Node g = make_real_variable("g"); |
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Node l = make_real_variable("l"); |
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Node q = make_real_variable("q"); |
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Node s = make_real_variable("s"); |
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Node u = make_real_variable("u"); |
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a.emplace_back(l == mone); |
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a.emplace_back(!(g * s == zero)); |
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a.emplace_back(q * s == zero); |
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a.emplace_back(u == zero); |
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a.emplace_back(q == (one + (fifth * g * s))); |
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a.emplace_back(l == u + q * s + (fifth * g * s * s)); |
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test_delta(a); |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_delta_two) |
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{ |
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std::vector<Node> a; |
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Node zero = d_nodeManager->mkConst(Rational(0)); |
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Node one = d_nodeManager->mkConst(Rational(1)); |
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Node mone = d_nodeManager->mkConst(Rational(-1)); |
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Node fifth = d_nodeManager->mkConst(Rational(1, 2)); |
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Node g = make_real_variable("g"); |
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Node l = make_real_variable("l"); |
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Node q = make_real_variable("q"); |
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Node s = make_real_variable("s"); |
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Node u = make_real_variable("u"); |
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|
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a.emplace_back(l == mone); |
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a.emplace_back(!(g * s == zero)); |
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a.emplace_back(u == zero); |
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a.emplace_back(q * s == zero); |
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a.emplace_back(q == (one + (fifth * g * s))); |
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a.emplace_back(l == u + q * s + (fifth * g * s * s)); |
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|
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test_delta(a); |
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} |
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TEST_F(TestTheoryWhiteArithCAD, test_ran_conversion) |
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{ |
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RealAlgebraicNumber ran( |
405 |
4 |
std::vector<Rational>({-2, 0, 1}), Rational(1, 3), Rational(7, 3)); |
406 |
|
{ |
407 |
4 |
Node x = make_real_variable("x"); |
408 |
4 |
Node n = nl::ran_to_node(ran, x); |
409 |
4 |
RealAlgebraicNumber back = nl::node_to_ran(n, x); |
410 |
2 |
EXPECT_TRUE(ran == back); |
411 |
|
} |
412 |
2 |
} |
413 |
42 |
} // namespace cvc5::test |
414 |
|
|
415 |
|
#endif |